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values of m^T C^-1 m for array mean=0, variance=1
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| Repeat of https://gist.github.com/evanbiederstedt/a763375f068b05167c26 | |
| with vector array of shape (3072,), mean=0, variance=1 | |
| tempp = np.random.normal(0.0, 1.0, 3072) # mean = 0, std = 1 = var = 1 | |
| # Test 1 | |
| vary_x_samples125 = np.logspace(-8, -12, num=40) # C3 parameter, vary from e-08 to e-12 | |
| sigma125 = 5e-22 # chose this sigma^2 parameter, hold constant | |
| #FIRST, NO PEAK CODE, i.e. scale covariance matrix by e+21 | |
| #CODE | |
| #https://gist.github.com/evanbiederstedt/a763375f068b05167c26 | |
| # | |
| # Hold sigma^2 constant, vary C3 | |
| # | |
| OUTPUT | |
| m^T c^-1 m terms are | |
| [ 6063.03944238 6239.6867014 6186.70223744 6238.94664056 6191.4244392 | |
| 6176.35233904 6169.08917136 6168.06081044 6160.040556 6161.52378429 | |
| 6161.94142132 6159.40639312 6158.72308258 6159.40443733 6158.8283143 | |
| 6159.45252001 6159.05305479 6159.32630012 6158.87793763 6158.98306791 | |
| 6159.08544029 6158.81735827 6158.96626508 6158.89501335 6158.97620424 | |
| 6158.9274596 6158.88636871 6158.90387669 6158.91760602 6158.90812902 | |
| 6158.90325582 6158.90071489 6158.90624671 6158.89835533 6158.90613525 | |
| 6158.89200745 6158.89331928 6158.89317107 6158.89402207 6158.89378695] | |
| ****************** | |
| logdetC terms are | |
| [-1910.79269502 -1899.49346143 -1894.31400072 -1893.9865907 -1890.0321336 | |
| -1889.55785882 -1889.79498435 -1890.52858638 -1891.04930553 -1892.56437866 | |
| -1893.64297778 -1895.06109716 -1896.61902812 -1898.36601353 -1899.78459156 | |
| -1901.39518245 -1903.05163531 -1904.67733691 -1906.32176722 -1907.95386497 | |
| -1909.59522293 -1911.21625436 -1912.86998408 -1914.50988852 -1916.15690315 | |
| -1917.81120861 -1919.462296 -1921.10832586 -1922.76238417 -1924.41349353 | |
| -1926.06744684 -1927.71856858 -1929.37104233 -1931.02466563 -1932.67642731 | |
| -1934.32805631 -1935.98147704 -1937.63429343 -1939.28755537 -1940.94054106] | |
| ****************** | |
| Npix2pi term is | |
| 19301.9452637 | |
| ******************************************************************************* | |
| ******************************************************************************* | |
| # Test 2 | |
| vary_x_samples123 = np.logspace(-8, -12, num=40) # C3 parameter, vary from e-08 to e-12 | |
| sigma123 = 5e-22 # chose this sigma^2 parameter, hold constant | |
| #SECOND, THERE IS A PEAK CODE, i.e. scale covariance matrix by e+22 | |
| #CODE | |
| # | |
| # Hold sigma^2 constant, vary C3 | |
| # | |
| OUTPUT: | |
| m^T c^-1 m terms are | |
| [ 619.62979688 630.75762714 624.33641024 646.42781419 630.83033316 | |
| 628.42196746 628.01224636 627.30792608 627.08883245 626.63108718 | |
| 626.86471702 626.58633689 626.45310587 626.48049364 626.49818424 | |
| 626.41093951 626.44859437 626.38258585 626.37143213 626.3696847 | |
| 626.35372623 626.35473303 626.34452735 626.35210835 626.34802669 | |
| 626.34394785 626.34583766 626.33944449 626.34105563 626.34079913 | |
| 626.33981216 626.33885527 626.33921146 626.33861005 626.33822696 | |
| 626.33776682 626.33786979 626.33772158 626.33777337 626.33755162] | |
| ****************** | |
| logdetC terms are | |
| [ 5162.11916985 5174.89668376 5179.54501215 5178.57071109 5182.81051551 | |
| 5184.46873299 5183.19398907 5183.19703352 5182.37013867 5181.01067721 | |
| 5179.97913256 5178.52226416 5176.80653401 5175.16623507 5173.76193185 | |
| 5172.11691893 5170.45643259 5168.87473124 5167.23262542 5165.6055479 | |
| 5163.95696043 5162.3116691 5160.67301514 5159.02720484 5157.37926926 | |
| 5155.73010752 5154.07978174 5152.43292945 5150.77874406 5149.12856074 | |
| 5147.47438028 5145.82296635 5144.17003878 5142.51772009 5140.86502619 | |
| 5139.21290009 5137.56004832 5135.9069266 5134.25393896 5132.60101615] | |
| ****************** | |
| Npix2pi term is | |
| 19301.9452637 | |
| ******************************************************************************* | |
| ******************************************************************************* | |
| # Test 3 | |
| vary_x_samples125 = 5e-10 | |
| sigma125 = np.logspace(-21, -23, num=40) | |
| #We can do the same tests with holding C3 and varying the sigma^2 noise parameter: | |
| # | |
| #First use C3 = 5e-10, and then try 10% less, i.e. C3=4.5e-10 | |
| # | |
| #FIRST CODE, fix C3 = 5e-10 | |
| # | |
| #Hold C3 fixed, then do test again with 10% less C3 value | |
| #We use C3 = 5e-10 | |
| # | |
| OUTPUT: | |
| m^T c^-1 m terms are | |
| [ 3056.20931539 3439.33358524 3870.46710341 4355.78041819 | |
| 4902.49532247 5516.49235235 6207.96349215 6986.28116913 | |
| 7863.01494373 8849.09701467 9958.5489499 11208.36540772 | |
| 12619.22019092 14197.26767573 15981.25054659 17990.42802844 | |
| 20245.96573985 22786.47797877 25658.41585925 28882.50986532 | |
| 32508.44324612 36620.25796131 41214.54053757 46451.3399304 | |
| 52451.3607927 59281.97126605 58140.43064709 73849.68519667 | |
| 83596.33544031 94564.52774417 106607.70915675 120938.12045667 | |
| 136999.05138901 155621.00980102 172488.83210862 197269.6566713 | |
| 226064.62122472 258114.03947093 304914.6451813 341068.83724127] | |
| **************** | |
| logdetC terms are | |
| [ 226.9052794 -135.07131727 -496.90121724 -858.84168741 | |
| -1220.95683913 -1583.00135661 -1944.915235 -2306.69141473 | |
| -2668.93133159 -3030.70976015 -3393.04701702 -3754.86449285 | |
| -4117.08237295 -4478.81252165 -4840.70266103 -5203.60698497 | |
| -5565.30740991 -5927.80221985 -6289.9127427 -6652.62034049 | |
| -7016.06626191 -7378.97770017 -7739.66767859 -8103.60482614 | |
| -8468.13642146 -8832.06627575 -9201.75852318 -9558.79338163 | |
| -9920.82765381 -10286.47587538 -10655.88535624 -11026.26666575 | |
| -11395.66670283 -11762.37585804 -12132.20128441 -12499.66763487 | |
| -12883.12465843 -13266.56868972 -13654.89410426 -14040.44010189] | |
| ****************** | |
| Npix2pi term is | |
| 19301.9452637 | |
| ******************************************************************************* | |
| ******************************************************************************* | |
| # Test 4 | |
| vary_x_samples125 = 5e-10 | |
| sigma125 = np.logspace(-21, -23, num=40) | |
| #SECOND CODE, C3 fixed to 4.5e-10 | |
| # | |
| #Hold C3 fixed, then do test again with 10% less C3 value | |
| #Now use C3 = 4.5e-10 | |
| # | |
| OUTPUT: | |
| m^T c^-1 m terms are | |
| [ 2912.91163678 3278.29157663 3688.78891476 4151.43962411 | |
| 4672.16804496 5257.82792359 5917.08851782 6658.35637171 | |
| 7494.04238153 8433.17194244 9490.53562282 10680.1940994 | |
| 12022.83862483 13528.0477834 15222.62005293 17146.82186255 | |
| 19285.36520843 21716.90840606 24438.46964114 27520.0535268 | |
| 30984.41701002 34901.11856995 39270.20493271 44270.69528356 | |
| 49941.7331173 56628.65356416 59901.59201949 70814.71217834 | |
| 80031.30268259 90459.24816214 102436.94217516 116056.63249007 | |
| 131915.66126694 156694.59393477 152811.80664743 183689.92516624 | |
| 211790.65295544 243259.40026702 285462.99321654 341562.38606682] | |
| **************** | |
| logdetC terms are | |
| [ 226.9052794 -135.07131727 -496.90121724 -858.84168741 | |
| -1220.95683913 -1583.00135661 -1944.915235 -2306.69141473 | |
| -2668.93133159 -3030.70976015 -3393.04701702 -3754.86449285 | |
| -4117.08237295 -4478.81252165 -4840.70266103 -5203.60698497 | |
| -5565.30740991 -5927.80221985 -6289.9127427 -6652.62034049 | |
| -7016.06626191 -7378.97770017 -7739.66767859 -8103.60482614 | |
| -8468.13642146 -8832.06627575 -9201.75852318 -9558.79338163 | |
| -9920.82765381 -10286.47587538 -10655.88535624 -11026.26666575 | |
| -11395.66670283 -11762.37585804 -12132.20128441 -12499.66763487 | |
| -12883.12465843 -13266.56868972 -13654.89410426 -14040.44010189] | |
| ****************** | |
| Npix2pi term is | |
| 19301.9452637 | |
| ******************************************************************************* | |
| ******************************************************************************* | |
| # Test 5 | |
| vary_x_samples123 = 5e-10 | |
| sigma123 = np.logspace(-22, -24, num=40) | |
| #FIRST, FIND NO PEAK IN LF, NOISE PARAMETERS E-22 TO E-24 | |
| # | |
| #CODE, C3 = 5e-10: | |
| # | |
| #Hold C3 fixed, then do test again with 10% less C3 value | |
| #Use C3=5e-10 | |
| # | |
| #Noise is now varied from e-22 to e-24 | |
| # | |
| OUTPUT: | |
| m^T c^-1 m terms are | |
| [ 3115.80676984 3509.43859015 3951.18169027 4450.30837947 | |
| 5018.22687418 5669.12296358 6512.39354618 7035.64871188 | |
| 8017.42106036 9081.78915341 10246.3544283 11614.36145183 | |
| 12813.43506509 14816.26445455 10972.80849967 18727.36016301 | |
| 21228.15458374 24314.36538203 27914.83552674 30777.17018509 | |
| 37065.30435071 45042.76970101 63665.81035839 66193.98108607 | |
| -222373.06068062 69519.41277427 134234.75456565 105181.51667804 | |
| 90691.96135331 86196.57060379 -97323.35753444 113565.86041873 | |
| 2965.81147655 193051.18658492 99617.72031856 119141.30217934 | |
| -95961.19547079 -33984.2067834 -8309.41726665 -4336.92334402] | |
| ****************** | |
| logdetC terms are | |
| [ 239.71699157 -122.71079135 -486.33852385 -849.25504606 | |
| -1212.4921126 -1576.26351061 -1944.85327619 -2305.753459 | |
| -2669.13822474 -3030.65420367 -3396.41771088 -3763.82736171 | |
| -4131.60575246 -4506.35071982 -4889.11466545 -5248.4037388 | |
| -5612.4490359 -5995.67825433 -6385.48032885 -6779.9332622 | |
| -7172.39370076 -7581.395549 -8041.60387949 -8517.11067861 | |
| -9002.83276846 -9446.49442793 -9839.83647962 -10172.92306214 | |
| -10420.76829252 -10623.50283171 -10792.24792309 -10928.10844176 | |
| -11027.19559602 -11100.06733525 -11170.65063404 -11215.66540551 | |
| -11261.93661065 -11284.43614935 -11306.60681018 -11326.08454794] | |
| ****************** | |
| Npix2pi term is | |
| 19301.9452637 | |
| ******************************************************************************* | |
| ******************************************************************************* | |
| # Test 6 | |
| vary_x_samples123 = 4.5e-10 | |
| sigma123 = np.logspace(-22, -24, num=40) | |
| #SECOND CODE, | |
| #C3 = 4.5e-10 | |
| # | |
| #Hold C3 fixed, then do test again with 10% less C3 value | |
| #Now use C3=4.5e-10 | |
| # | |
| #Noise is now varied from e-22 to e-24 | |
| # | |
| m^T c^-1 m terms are | |
| [ 2.98296571e+03 3.36090866e+03 3.78476827e+03 4.26532893e+03 | |
| 4.80494553e+03 5.41825219e+03 6.13718240e+03 7.32181220e+03 | |
| 7.58478814e+03 8.64215882e+03 9.76004961e+03 1.10981090e+04 | |
| 1.27425089e+04 1.35173429e+04 1.58250781e+04 1.78044260e+04 | |
| 1.99491636e+04 2.29589521e+04 2.61711220e+04 3.03112591e+04 | |
| 2.79374840e+04 4.00573536e+04 4.84547156e+04 4.88975460e+04 | |
| 6.47920720e+04 1.05957459e+05 9.17710292e+04 1.41471647e+03 | |
| 5.31272340e+04 1.17311577e+05 4.41539020e+04 -1.20015118e+05 | |
| 2.81598852e+04 -1.51603586e+03 1.80542789e+05 -4.05951829e+04 | |
| 2.93604015e+05 -4.78810033e+04 -6.22225138e+03 -1.71448966e+06] | |
| ****************** | |
| logdetC terms are | |
| [ 238.87906146 -123.59978549 -486.97635053 -849.54919459 | |
| -1212.63010956 -1576.01604717 -1942.33073337 -2309.73321034 | |
| -2670.91431763 -3031.09627919 -3396.32588831 -3762.14204865 | |
| -4128.07960518 -4502.34341668 -4872.33980536 -5255.02597355 | |
| -5607.79232715 -5986.94061374 -6370.62068917 -6753.73665052 | |
| -7147.26442618 -7537.878678 -7981.39859695 -8433.45165572 | |
| -8907.83987127 -9384.80250567 -9848.92410084 -10252.021386 | |
| -10558.32732388 -10804.17249772 -11029.95815536 -11179.59272393 | |
| -11324.19494314 -11416.3809462 -11503.90735819 -11568.77486146 | |
| -11622.48104156 -11656.23132841 -11687.85082231 -11713.95931238] | |
| ****************** | |
| Npix2pi term is | |
| 19301.9452637 | |
| ******************************************************************************* | |
| ******************************************************************************* | |
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How the covariance matrix is scaled:
Test 1 scales Cij by (1e21)
Test 2 scales Cij by (1e22)
Test 3 and Test 4 scales by (1e21)
Test 4 and Test 5 scales by (1e22).